blob: 21c0f937d60529e89921f1eae9d0de2b2f7ebf9b [file] [log] [blame]
 /* s_tanhl.c -- long double version of s_tanh.c. * Conversion to long double by Ulrich Drepper, * Cygnus Support, drepper@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* Changes for 128-bit long double contributed by Stephen L. Moshier */ /* tanhq(x) * Return the Hyperbolic Tangent of x * * Method : * x -x * e - e * 0. tanhq(x) is defined to be ----------- * x -x * e + e * 1. reduce x to non-negative by tanhq(-x) = -tanhq(x). * 2. 0 <= x <= 2**-57 : tanhq(x) := x*(one+x) * -t * 2**-57 < x <= 1 : tanhq(x) := -----; t = expm1q(-2x) * t + 2 * 2 * 1 <= x <= 40.0 : tanhq(x) := 1- ----- ; t=expm1q(2x) * t + 2 * 40.0 < x <= INF : tanhq(x) := 1. * * Special cases: * tanhq(NaN) is NaN; * only tanhq(0)=0 is exact for finite argument. */ #include "quadmath-imp.h" static const __float128 one = 1.0, two = 2.0, tiny = 1.0e-4900Q; __float128 tanhq (__float128 x) { __float128 t, z; uint32_t jx, ix; ieee854_float128 u; /* Words of |x|. */ u.value = x; jx = u.words32.w0; ix = jx & 0x7fffffff; /* x is INF or NaN */ if (ix >= 0x7fff0000) { /* for NaN it's not important which branch: tanhq(NaN) = NaN */ if (jx & 0x80000000) return one / x - one; /* tanhq(-inf)= -1; */ else return one / x + one; /* tanhq(+inf)=+1 */ } /* |x| < 40 */ if (ix < 0x40044000) { if (u.value == 0) return x; /* x == +- 0 */ if (ix < 0x3fc60000) /* |x| < 2^-57 */ { math_check_force_underflow (x); return x * (one + tiny); /* tanh(small) = small */ } u.words32.w0 = ix; /* Absolute value of x. */ if (ix >= 0x3fff0000) { /* |x| >= 1 */ t = expm1q (two * u.value); z = one - two / (t + two); } else { t = expm1q (-two * u.value); z = -t / (t + two); } /* |x| > 40, return +-1 */ } else { z = one - tiny; /* raised inexact flag */ } return (jx & 0x80000000) ? -z : z; }